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October, 1981 Some Results on the LIL in Banach Space with Applications to Weighted Empirical Processes
V. Goodman, J. Kuelbs, J. Zinn
Ann. Probab. 9(5): 713-752 (October, 1981). DOI: 10.1214/aop/1176994305

Abstract

We examine the cluster set of $S_n/a_n$ for Banach space valued random variables, and investigate the relationship between the central limit theorem and the law of the iterated logarithm in this setting. In the case of Hilbert space valued random variables, necessary and sufficient conditions are given for the law of the iterated logarithm. Some interesting examples are also included. We then apply our results to weighted empiricals both in the supremum norm and the $L^2\lbrack 0, 1\rbrack$ norm.

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V. Goodman. J. Kuelbs. J. Zinn. "Some Results on the LIL in Banach Space with Applications to Weighted Empirical Processes." Ann. Probab. 9 (5) 713 - 752, October, 1981. https://doi.org/10.1214/aop/1176994305

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0472.60004
MathSciNet: MR628870
Digital Object Identifier: 10.1214/aop/1176994305

Subjects:
Primary: 60B05
Secondary: 28A40, 60B10, 60F05, 60F10, 60F15

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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